Group #14565140 — subgroups

Subgroups — #14565140

Order 2432.

176 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926587	C₂	1	2	yes	maximal
2	C₂×#10597275	C₂	1	1	yes	maximal, characteristic
3	#11926312	C₂	1	2	yes	maximal
4	#11926309	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#424	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#117	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	C₂×#64520	C₂²	1	2	yes	—
11	C₁₉×C₄⋊C₈	—	2	2	no	—
12	#10597275	—	2	2	no	—
13	#10597265	—	2	2	no	—
14	#10597264	—	2	2	no	—
15	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
16	C₂²×Dic₁₉	—	2	2	no	—
17	M₁₆×C₁₉	—	2	2	no	—
18	C₂×C₈×C₁₉	—	2	2	no	—
19	C₂×C₈×C₁₉	—	2	1	no	—
20	C₂×C₈×C₁₉	D₄	1	2	yes	—
21	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂²⋊C₄×C₁₉	—	2	1	no	—
24	C₄²×C₁₉	—	2	1	no	—
25	C₄⋊Dic₁₉	—	2	2	no	—
26	C₄⋊Dic₁₉	—	2	2	no	—
27	#64520	—	2	2	no	—
28	#64520	Q₈	1	4	yes	—
29	C₂×C₁₉⋊C₈	—	2	2	no	—
30	C₂³×C₁₉	#41	1	1	yes	characteristic
31	C₂×C₄×C₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
36	C₂×C₄×C₁₉	#41	1	2	yes	—
37	C₂×Dic₁₉	—	4	2	no	—
38	C₂×Dic₁₉	—	8	2	no	—
39	C₈×C₁₉	—	2	2	no	—
40	C₈×C₁₉	—	4	1	no	—
41	C₁₉⋊C₈	—	2	4	no	—
42	#2089	—	19	1	no	maximal, Sylow
43	C₂²×C₁₉	—	2	1	no	—
44	C₂²×C₁₉	—	2	1	no	—
45	C₂²×C₁₉	#121	1	1	yes	characteristic
46	C₂²×C₁₉	#125	1	2	yes	—
47	C₄×C₁₉	—	4	1	no	—
48	C₄×C₁₉	—	4	1	no	—
49	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
50	C₄×C₁₉	#123	1	1	yes	characteristic
51	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
52	Dic₁₉	—	8	2	no	—
53	#428	—	19	2	no	—
54	C₂×#107	—	19	1	no	—
55	#424	D₁₉	1	1	yes	characteristic
56	#343	—	19	2	no	—
57	#341	—	19	1	no	—
58	C₂×C₁₉	—	2	2	no	—
59	C₂×C₁₉	#398	1	1	yes	characteristic
60	C₂×C₁₉	#472	1	1	yes	characteristic
61	C₂×C₁₉	#473	1	1	yes	characteristic
62	C₂×M₁₆	—	19	2	no	—
63	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
64	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
65	#117	C₂×D₁₉	1	1	yes	characteristic
66	C₂×C₄⋊C₄	—	19	2	no	—
67	#107	—	38	2	no	—
68	#107	—	38	2	no	—
69	#106	—	38	2	no	—
70	C₄⋊C₈	—	2	2	no	—
71	C₁₉	#2089	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₄	—	38	2	no	—
73	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
74	M₁₆	—	2	2	no	—
75	M₁₆	—	19	4	no	—
76	M₁₆	—	38	2	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	1	no	—
79	C₂×C₈	—	38	2	no	—
80	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
81	C₄⋊C₄	—	38	2	no	—
82	C₄⋊C₄	—	38	2	no	—
83	C₄⋊C₄	D₇₆	1	1	yes	characteristic
84	C₄⋊C₄	D₇₆	1	1	yes	characteristic
85	C₂²⋊C₄	—	2	1	no	—
86	C₄²	—	2	1	no	—
87	C₂³	#64541	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	76	2	no	—
91	C₂×C₄	—	152	2	no	—
92	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
93	C₂×C₄	#64543	1	2	yes	—
94	C₂×C₄	Q₈×D₁₉	1	2	yes	—
95	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
96	C₈	—	2	2	no	—
97	C₈	—	4	1	no	—
98	C₈	—	38	4	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	#10597335	1	2	yes	—
102	C₂²	#10597376	1	1	yes	characteristic
103	C₄	—	4	1	no	—
104	C₄	—	4	1	no	—
105	C₄	—	152	2	no	—
106	C₄	#10597343	1	2	yes	—
107	C₄	#10597381	1	1	yes	characteristic
108	C₄	#10597390	1	1	yes	characteristic
109	C₂	—	2	2	no	—
110	C₂	#11926474	1	1	yes	characteristic
111	C₂	#11926814	1	1	yes	characteristic
112	C₂	#11926819	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926587

C₂

yes

maximal

C₂×#10597275

C₂

yes

maximal, characteristic

#11926312

C₂

yes

maximal

#11926309

C₂

yes

maximal, characteristic

C₁₉×#424

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×#64520

C₂²

yes

—

C₁₉×C₄⋊C₈

—

#10597275

—

#10597265

—

#10597264

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

#64520

Q₈

yes

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2089

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

#125

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

#123

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

Dic₁₉

—

#428

—

C₂×#107

—

#424

D₁₉

yes

characteristic

#343

—

#341

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

#117

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

#107

—

#107

—

#106

—

C₄⋊C₈

—

C₁₉

#2089

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₇₆

yes

characteristic

C₄⋊C₄

D₇₆

yes

characteristic

C₂²⋊C₄

—

C₄²

—

C₂³

#64541

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

152

—

C₂×C₄

C₂×D₇₆

yes

characteristic

C₂×C₄

#64543

yes

—

C₂×C₄

Q₈×D₁₉

yes

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

100

C₂²

—

101

C₂²

#10597335

yes

—

102

C₂²

#10597376

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

152

—

106

C₄

#10597343

yes

—

107

C₄

#10597381

yes

characteristic

108

C₄

#10597390

yes

characteristic

109

C₂

—

110

C₂

#11926474

yes

characteristic

111

C₂

#11926814

yes

characteristic

112

C₂

#11926819

yes

characteristic

	subgroup	G/H
center	C₂²	#10597376
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#424	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂³×C₁₉	#41
hypercenter	#424	D₁₉
hypocenter	C₁₉	#2089
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

subgroup

G/H

center

C₂²

#10597376

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#424

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

N	H ≅ G/N	type
71. C₁₉	#2089	semidirect

H ≅ G/N

type

71. C₁₉

#2089

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11926587	2
C₂×#10597275	2
#11926312	2
#11926309	2
C₁₉×#424	2
#2089	19

subgroup

index

C₁₉×#424

Subgroups — #14565140

Conjugacy classes of subgroups

Complements

Maximal subgroups